Question: Simplify the following expression: $a = \dfrac{z^2 - 3z - 54}{z + 6} $
Explanation: First factor the polynomial in the numerator. $ z^2 - 3z - 54 = (z + 6)(z - 9) $ So we can rewrite the expression as: $a = \dfrac{(z + 6)(z - 9)}{z + 6} $ We can divide the numerator and denominator by $(z + 6)$ on condition that $z \neq -6$ Therefore $a = z - 9; z \neq -6$